3.8 Inverse Rotation Compelled by External Torque Imposed …
59
not under the physiological condition) but the solution is still under the condition
that the ATP hydrolysis reaction should occur, ΔG =−20k B T (T = 298 K) but ΔG
< 0 is still true. Theoretically, W = −ΔG holds irrespective of the ATP, ADP, and Pi
concentrations. In fact, Muneyuki and coworkers found that W = −ΔG holds at all
the ATP, ADP, and Pi concentrations tested [34].
The experimental observations in case III indicated that as the external torque
becomes stronger, the apparent rotation rate increases [34]. The free-energy balance
can be discussed in a manner which is similar to that in case I. All the normal,
inverse, and stopped rotations should occur. With an increase in torque strength, the
proportion of the normal rotation becomes lower. With a further increase in torque
strength, the proportion of the stopped rotation also becomes lower. Once the torque
becomes sufficiently strong, the inverse rotation occurs almost exclusively.
3.8.4 Substantially Different Behavior Observed for a Mutant
of F 1 -ATPase
Muneyuki and coworkers [35] carried out interesting experiments using a mutant of
F 1 -ATPase. In this mutant, a mutation of E190D is made for every β subunit. The
residue E190 is located near the γ-phosphate of ATP bound to the catalytic site and
significantly affects the ATPase activity [36]. The cleavage of the β−γ-phosphate
bond of ATP is markedly delayed by the mutation, resulting in the long catalytic
dwell [24]. In what follows, we summarize the experimental results obtained for the
mutant and comment on them.
(i) The mutant cannot form a stabilized structure without the γ subunit [35]. This
result suggests that it is not achievable to closely pack the α−β interfaces of the
α 3 β 3 complex and the packing efficiencies of the three β subunits are not well
reflected on those of subcomplexes I−γ, II−γ, and III−γ. In comparison with
the wild type, the structural stability of the α 3 β 3 complex is less influenced by
the chemical compound bound to each β subunit.
(ii) With the γ subunit, the mutant forms a stable complex [35]. The α 3 β 3 γ complex
of the mutant is capable of hydrolyzing ATP into ADP and Pi with the rotation
of the γ subunit in the normal direction under the solution condition that the ATP
hydrolysis reaction occurs. However, the thermal denaturation temperature of
the mutant is significantly lower than that of the wild type [35]. This result
indicates that the α 3 β 3 γ complex of the mutant is less stable than that of the
wild type. In the mutant, the orientation of the γ subunit is less correlated with
the packing structure of the α 3 β 3 complex.
(iii) By the application of external torque to the γ subunit, the rotation essentially
vanishes with an external torque which is considerably weaker than for the wild
type [35]. Let W Wild and W Mutant be the values of W with which the rotation
essentially vanishes for the wild type and the mutant, respectively. From the
experimental result mentioned above, W Mutant < W Wild . Since the values of ΔG
59
not under the physiological condition) but the solution is still under the condition
that the ATP hydrolysis reaction should occur, ΔG =−20k B T (T = 298 K) but ΔG
< 0 is still true. Theoretically, W = −ΔG holds irrespective of the ATP, ADP, and Pi
concentrations. In fact, Muneyuki and coworkers found that W = −ΔG holds at all
the ATP, ADP, and Pi concentrations tested [34].
The experimental observations in case III indicated that as the external torque
becomes stronger, the apparent rotation rate increases [34]. The free-energy balance
can be discussed in a manner which is similar to that in case I. All the normal,
inverse, and stopped rotations should occur. With an increase in torque strength, the
proportion of the normal rotation becomes lower. With a further increase in torque
strength, the proportion of the stopped rotation also becomes lower. Once the torque
becomes sufficiently strong, the inverse rotation occurs almost exclusively.
3.8.4 Substantially Different Behavior Observed for a Mutant
of F 1 -ATPase
Muneyuki and coworkers [35] carried out interesting experiments using a mutant of
F 1 -ATPase. In this mutant, a mutation of E190D is made for every β subunit. The
residue E190 is located near the γ-phosphate of ATP bound to the catalytic site and
significantly affects the ATPase activity [36]. The cleavage of the β−γ-phosphate
bond of ATP is markedly delayed by the mutation, resulting in the long catalytic
dwell [24]. In what follows, we summarize the experimental results obtained for the
mutant and comment on them.
(i) The mutant cannot form a stabilized structure without the γ subunit [35]. This
result suggests that it is not achievable to closely pack the α−β interfaces of the
α 3 β 3 complex and the packing efficiencies of the three β subunits are not well
reflected on those of subcomplexes I−γ, II−γ, and III−γ. In comparison with
the wild type, the structural stability of the α 3 β 3 complex is less influenced by
the chemical compound bound to each β subunit.
(ii) With the γ subunit, the mutant forms a stable complex [35]. The α 3 β 3 γ complex
of the mutant is capable of hydrolyzing ATP into ADP and Pi with the rotation
of the γ subunit in the normal direction under the solution condition that the ATP
hydrolysis reaction occurs. However, the thermal denaturation temperature of
the mutant is significantly lower than that of the wild type [35]. This result
indicates that the α 3 β 3 γ complex of the mutant is less stable than that of the
wild type. In the mutant, the orientation of the γ subunit is less correlated with
the packing structure of the α 3 β 3 complex.
(iii) By the application of external torque to the γ subunit, the rotation essentially
vanishes with an external torque which is considerably weaker than for the wild
type [35]. Let W Wild and W Mutant be the values of W with which the rotation
essentially vanishes for the wild type and the mutant, respectively. From the
experimental result mentioned above, W Mutant < W Wild . Since the values of ΔG